Circles and the Compass

The Circle

A circle is a simple closed curve where every point on the curve is at the same distance from a fixed point inside it.

Using a Compass

A compass has a metal tip and a pencil tip. To draw a circle:

1. Fix the needle: Place the sharp metal tip at the point you want to be the center.
2. Set the radius: Open the compass so the distance between the needle and the pencil tip matches your desired radius (e.g., 4 cm).
3. Rotate: Spin the compass to draw the curve.

Visual Representation

Here is a circle with center $P$ and a radius of 4 units.

Thinking about Distance

If you mark a point $P$ and want to find all points that are exactly 4 cm away from $P$, they will form a circle.

• Points inside the circle are less than 4 cm from $P$.
• Points outside the circle are more than 4 cm from $P$.
• Points on the circle are exactly 4 cm from $P$.